My company, Mangoesmapping, is a PB business partner here in Australia and have a client reporting the same issue as Stuart, with a Local Government using IE. It gets to the point that even vector tiles of low density data load impossibly slowly.
Issue is possibly complicated through access via Citrix. Each user's virtual machine is only provisioned with 2GB memory and IE cache can get bloated from many different web apps accessed during a long session.
This issue is definitely linked to IE. I haven't replicated on other browsers.
Logging out to dump IE cache usually improves performance for our end users, although that action is unintuitive for naive users and inconvenient.
Cheers, Al.